Vibration generation is a common means by which products are tested in their development and manufacturing stages. Most products will encounter some form of environmental vibration throughout their lifecycle. Vibration testing is used to ensure product integrity in anticipation of vibrations that may be present, for example, during transportation and in-service use. Any given product will likely be subject to a variety of vibration environments. If a device is mounted in an automobile, for example, then it will have to withstand vibration from driving on various road and terrain surfaces. It is rarely possible to test products in their in-situ environments, so these environments must be simulated with mechanical test systems. A common method of this simulation is with a Random Vibration Controller, which generates a random vibration with a frequency content tailored to match the expected frequency content of the anticipated real-world environment.
In U.S. Pat. No. 3,710,082, E. Sloane and C. Heizman describe a test system that controls a vibratory shaker. The shaker consists of a single-axis, reciprocating, signal-controlled plunger or rod for simulating the vibration of a device under test supported by the shaker. An input signal, i.e. a voltage signal, operates the shaker with some amount of randomness and the shaker vibratory output is monitored. From recordings of the output, one may compute for given times, the statistical mean and the statistical moments of order n relative to the mean.
Most implementations of random vibration controllers generate vibrations that have a Gaussian (also called “normal”) amplitude distribution. The variance and frequency content of this vibration can be changed, but the shape of its distribution cannot. This Gaussian distribution is commonly used not because it is best at simulating real-world vibration environments, but because it occurs naturally from the most common ways of generating random waveforms. For resonant systems subjected to random vibration, it can be shown that the response tends to be approximately Gaussian even if the input is not.
However, the vibration occurring in many real world environments is not Gaussian, but has more and larger peaks than what would be predicted from a pure Gaussian distribution. A Gaussian random waveform will typically contain peaks no more than 4 times the RMS of the waveform, while real-world vibration may contain peaks 8 to 10 times the RMS level. Because of this, it is desirable to control the amplitude distribution of the generated vibration, in addition to the frequency content, for more realistic simulation.
Mathematically, the probability distributions that underlie random waveforms can be characterized by central moments. The computations are described, e.g., in the book “Mechanical Vibration and Shock, Random Vibration, Vol. III by C. Lalanne, 2002. The first central moment is always zero and the second central moment is the variance (equal to the square of the standard deviation). The third central moment, often called skewness when divided by the (3/2)-power of the variance, describes the asymmetry of the distribution about the mean.
The fourth central moment, called kurtosis when reduced by division with the square of the variance, is a measure indicative of the presence of peaks in the distribution. A random waveform with a higher kurtosis will contain more “outlier” peaks in the extremes of the distribution. Kurtosis is a scalar value, defined for a given probability distribution as its fourth central moment divided by the square of its second central moment (variance). As defined here, a pure Gaussian distribution always has a kurtosis of 3, while real-world vibration may have a kurtosis of 5 to 8. Because it relates to the frequency of occurrence of these extreme peaks, kurtosis is a useful measure to characterize the distribution of random vibration.
In the aforementioned '082 patent of Sloane and Heizman, the shaker output signal is converted to a digital power spectral density in the frequency domain that is compared to a reference value for output to a multiplier that applies a random phase angle argument before conversion back to the time domain as a driving signal to the shaker. Thus, while the input to the shaker has a random phase angle as part of the driver, feedback from the shaker is used to control the power spectral density of the vibration.
In U.S. Pat. No. 7,426,426, P. Van Baren teaches a test system similar to Sloane et al. but with two parallel feedback loops. In one loop the power spectral density is compared to a reference value, while in a second loop a kurtosis measurement is compared to a reference kurtosis before being applied to a white noise or random signal generator. Thus, Van Baren not only controls the power spectral density of the vibration, but also uses the feedback to apply a bias to the white noise that adjusts the kurtosis of the random vibration. The time signals from the two loops are combined using a convolution filter in the time domain to obtain the drive signal for the shaker.
A similar, but more sophisticated, approach is used by J. Zhuge in published application U.S. 2010/0305886 where kurtosis more strongly influences the input signal by its presence in more than one feedback loop and both Gaussian and non-Gaussian spectrum generators are used in the different loops.
There are other inventions in the prior art that attempt to control kurtosis with different methods. One such method involves generating a random time stream through conventional means, and then applying a non-linear transform to change the distribution. Although this is effective for controlling the distribution, it adds non-linear distortion to the signal and changes its spectral content. Another method involves superimposing shock waveforms over the generated random waveform to add peaks, but this also distorts the spectral content of the signal.
An object of the invention is to devise a vibration control system for a shaker that gives appropriate weight to both the power spectral density and to statistical aspects of the random amplitude distribution.